Probabilistic fracture mechanics analysis of spalling during edge indentation in ice

The design of marine structures for ice environments requires ice load estimates, which are greatly influenced by fracture and associated scale effects. During edge indentation of natural ice, fracture processes are highly influenced by variability associated with flaw structure and contact conditions. A probabilistic framework is the most appropriate for modeling such interactions. In the present analysis, a probabilistic fracture mechanics model has been developed to model localized fracture events for ice specimens with ice edge taper angles ranging from 0° to 45°. Crack instability criteria have been formulated for compressive and tensile states of stress. This approach varies from traditional probabilistic failure models which assume that zones of compressive stress have zero failure probability and include only tensile zones in the calculation of failure probability. For compressive edge loading, experimental results indicate that local edge fractures (spalls) are most likely to emanate from regions of the ice where cracks would be subjected to axial compression and lateral tension. Compressive contact loads required to propagate fractures from zones of bi-axial tension or bi-axial compression were found to be considerably higher and are much less probable. Estimates of the mean pressure required to trigger a fracture event as a function of ice thickness were generated for thicknesses in the range of 0.2–2.0 m. These results demonstrate that observed scale effects in ice pressure data can be explained by probabilistic aspects of fracture. Simulations of fracture probabilities as a function of loading eccentricity confirmed that extreme loads of interest in engineering design are most likely to correspond to high pressure zones located near the center of thickness of the ice sheet. Results indicate that fractures occur more readily for flat ice edges and higher pressures are required to propagate fractures for edges with more highly tapered edges. This result provides a theoretical basis to explore the interplay between fracture and crushing, both of which occur during compressive ice failure: fractures create tapered edges that localize contact in manner that supports crushing; crushing, over several cycles, flattens the ice edge in a manner that in turn promotes fracture. While the application presented here is focused on ice mechanics, the analysis methodology could readily be applied to other brittle materials.